Typical Utility Functions Research Articles

Optimal asset allocation in retirement planning: threshold-based utility maximization

PurposeThe aim of this paper is to modify the shape of utility functions traditionally used in expected utility theory (EUT) to derive optimal retirement saving decisions. Inspired by current reference point based approaches, the authors argue that utility functions with jumps or kinks at certain threshold points might very well be rational.Design/methodology/approachThe authors suggest an alternative to typical utility functions used in EUT, to be applied in the context of retirement saving decisions. The authors argue that certain elements that are used to model biases in behavioral models should–in the context of optimal retirement saving decisions–be considered “rational” and hence be included in a normative setting as well. The authors compare the optimal asset allocation derived under such utility functions with results under traditional power utility.FindingsThe authors find that the considered threshold levels can have a significant impact on the optimal investment decision for some individuals. In particular, the authors show that a much riskier investment than under EUT can become optimal if some level of income is secured by a social security and a significant portion of the distribution of terminal wealth lies below this level.Originality/valueContrary to previous work, this model is especially designed to assess the question of optimal product choice/asset allocation in the specific setting of retirement planning and from a normative point of view. In this regard, the authors first motivate the use of several thresholds and then apply this approach in a capital market model with stochastic stocks and stochastic interest rates to two illustrative investment alternatives.

WEIGHTED QUASI-ARITHMETIC MEANS AND A RISK INDEX FOR STOCHASTIC ENVIRONMENTS

In this paper, the weighted quasi-arithmetic means are discussed from the viewpoint of utility functions and downward risks in economics. Representing the weighting functions by probability density functions and the conditional expectations, an index for downward risks in stochastic environments is derived. This paper discusses the relation among the index, the first-order stochastic dominance and the risk premium in economics, and further it investigates the relation between the index and value-at-risks which are known as another estimation for downward risks in finance. Finally, this paper shows a lot of examples of the weighted quasi-arithmetic mean and the aggregated mean ratio for various typical utility functions with various typical utility functions and probability density functions.

Quasi-arithmetic means and ratios of an interval induced from weighted aggregation operations

In this paper we deal with weighted quasi-arithmetic means of an interval using utility functions in decision making. The mean values are discussed from the viewpoint of weighted aggregation operators, and they are given as weighted aggregated values of each point in the interval. The properties of the weighted quasi-arithmetic mean and its translation invariance are investigated. For the application in economics, we demonstrate the decision maker’s attitude based on his utility by the weighted quasi-arithmetic mean and the aggregated mean ratio. Several examples of the weighted quasi-arithmetic mean and the aggregated mean ratio for various typical utility functions are shown to understand our motivation and for the applications in decision making.

Risk attitudes and risky behavior

In economic theory, risk aversion is a characteristic of the typical utility function of money. Observations of how people deal with risks in real life have cast some doubts on the prevalence of risk aversion. People buy insurance, but they also gamble and take investment risks. Many of the conclusions in the discussions of utility derive from experiments employing some kind of lottery choices. While the experiments have given interesting ideas for theory, there has been little testing of the extent to which the obtained measures of risk attitudes correlate with actual behavior. Data from the VSB panel were used to answer three questions: (1) Can hypothetical risky choice questions be meaningfully answered by ordinary survey respondents? (2) What are the relationships between different measures of risk attitudes and actual portfolio choices of risky assets? (3) What is the relationship between risk attitude and playing in lotteries, lotto, etc.?

Social utility and decision making in interpersonal contexts.

Three studies examined preferences for outcomes to self and a codisputant. Studies I and 2 estimated social utility functions from judgments of with alternative outcomes. Comparing functional forms, we found that a utility function, including terms for own payoff and for positive and negative discrepancies between the parties' payoffs (advantageous and disadvantageous inequality), provides a close fit to the data. The typical utility function is steeply increasing and convex for disadvantageous inequality and weakly declining and convex for advantageous inequality. We manipulated dispute type (personal, business) and disputant relationship (positive, neutral, or negative) and found that both strongly influence preferences for advantageous but not disadvantageous inequality. A third study contrasted implications of the social utility functions with predictions of individual utility theories. People care about the outcomes of others. We sacrifice our own interests to help loved ones or harm adversaries. Participants withdraw from profitable participation in a laboratory experiment if they perceive inequity in remuneration (Schmitt & Marweli, 1972). Players in two-person ultimatum games (in which one player proposes a distribution of a fixed amount of money that the other has the option of either accepting or rejecting) frequently reject a positive but inequitable offer even though the alternative is no gain at all (Guth, Schmittberger, & Schwarze, 1982). Negotiations between parties often collapse when one party becomes incensed with the other and attempts to maximize his opponent's displeasure rather than his own satisfaction (scigel & Fouraker, 1960, p. 100). In general, disputants are concerned not only with the outcomes they receive, but also with the outcomes of their opponents (Pruitt & Rubin, 1986).

On personal optimal sequential saving-consumption strategy A discrete system approach

The paper concerns a problem of determining a sequence of savings maximizing the total utility an individual gains during a predetermined period consisting of a finite number N of period units. The analysis carried out is based on methods which are usually used for engineering systems analysis. The forms of the savings and consumption sequences are first determined independently of the specific utility function. It is shown that the saving sequence should be concave and that optimal consumption should grow successively. Then, explicit sequences are given in closed form for a class of typical utility functions, for which further conclusions are drawn. The dependence of optimal consumption on income is affine, whereas that of saving is of a ‘ threshold ’ nature.